Theorem simpl3r 1037

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simpl3r	⊢ (((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜏) → 𝜓)

Proof of Theorem simpl3r

Step	Hyp	Ref	Expression
1		simp3r 1010	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	adantr 274	1 ⊢ (((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 103   ∧ w3a 962

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 964

This theorem is referenced by:  tfisi  4496  ltmul1a  8346  lemul1a  8609  xrbdtri  11038  dvdscmulr  11511  dvdsmulcr  11512  dvdsadd2b  11529